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A new barrier for a class of semidefinite problems

Published online by Cambridge University Press:  08 November 2006

Erik A. Papa Quiroz  and
Paolo Roberto Oliveira
Erik A. Papa Quiroz
Affiliation:
Programa de Engenharia de Sistemas e Computacão, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil; erik@cos.ufrj.br
Paolo Roberto Oliveira
Affiliation:
Programa de Engenharia de Sistemas e Computacão, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil; erik@cos.ufrj.br Rua Honorio, 1144 c 5, 20771-421, Rio de Janeiro, Brazil; poliveir@cos.ufrj.br
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Abstract

We introduce a new barrier function to solve a class ofSemidefinite Optimization Problems (SOP) with bounded variables.That class is motivated by some (SOP) as the minimization of thesum of the first few eigenvalues of symmetric matrices and graphpartitioning problems. We study the primal-dual central pathdefined by the new barrier and we show that this path is analytic,bounded and that all cluster points are optimal solutions of theprimal-dual pair of problems. Then, using some ideas fromsemi-analytic geometry we prove its full convergence. Finally, weintroduce a new proximal point algorithm for that class ofproblems and prove its convergence.

Keywords

Interior point methodsbarrier functioncentral pathsemidefinite optimization.
Type
Research Article
Information
RAIRO - Operations Research , Volume 40 , Issue 3 , July 2006 , pp. 303 - 323
Copyright
© EDP Sciences, 2006

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